Graduate Aptitude Test in Engineering (GATE) — Questions and Answers

Question 1: Which study approach is most effective for Signal Processing material?

Passive re-reading of notes
Active recall with practice questions (Correct answer)
Highlighting all text
Studying for very long sessions without breaks

Correct answer: Active recall with practice questions

Active recall through practice questions is the most effective study method, as it strengthens memory retrieval pathways.

Question 2: What role does ethics play in Signal Processing practice?

It guides professional conduct and protects stakeholders (Correct answer)
It only matters for legal compliance
It only applies to managers
Ethics is optional in professional settings

Correct answer: It guides professional conduct and protects stakeholders

Professional ethics provide frameworks for responsible decision-making, ensuring practitioners act in the best interest of those they serve.

Question 3: Find the odd one out: Apple, Banana, Carrot, Mango.

Mango
Carrot (Correct answer)
Apple
Banana

Correct answer: Carrot

Apple, Banana, and Mango are all types of fruits. Carrot, however, is a root vegetable. Therefore, 'Carrot' is the odd one out because it belongs to a different botanical category than the other items in the list.

Question 4: What is the scientific method?

A math formula
A way to write lab reports
A single experiment
A systematic process for investigating phenomena through observation, hypothesis, experimentation, and analysis (Correct answer)

Correct answer: A systematic process for investigating phenomena through observation, hypothesis, experimentation, and analysis

The scientific method is the structured approach scientists use: observe, question, hypothesize, experiment, analyze data, and draw conclusions.

Question 5: The average of five consecutive odd numbers is 45. What is the largest of these numbers?

49 (Correct answer)
47
53
51

Correct answer: 49

Middle number = 45 (average of consecutive odd numbers is the middle); five consecutive odds: 41,43,45,47,49; largest=49.

Question 6: What role does ethics play in Digital Logic practice?

It guides professional conduct and protects stakeholders (Correct answer)
It only matters for legal compliance
It only applies to managers
Ethics is optional in professional settings

Correct answer: It guides professional conduct and protects stakeholders

Professional ethics provide frameworks for responsible decision-making, ensuring practitioners act in the best interest of those they serve.

Question 7: What is the difference between a hypothesis and a theory?

A hypothesis cannot be tested
A theory is less certain than a hypothesis
A hypothesis is a testable prediction; a theory is a well-supported explanation (Correct answer)
They are the same thing

Correct answer: A hypothesis is a testable prediction; a theory is a well-supported explanation

A hypothesis is an educated guess that can be tested, while a theory is a broad explanation supported by extensive evidence from multiple experiments.

Question 8: What is encryption?

Backing up data
Deleting data
Compressing files
Converting data into coded format to prevent unauthorized access (Correct answer)

Correct answer: Converting data into coded format to prevent unauthorized access

Encryption transforms readable data into unreadable ciphertext using algorithms and keys, ensuring only authorized parties can access the information.

Question 9: If A is an n×n invertible matrix, which statement is FALSE?

Rank(A) = n
det(A) ≠ 0
The system Ax=0 has only the trivial solution
A has n linearly independent eigenvectors (Correct answer)

Correct answer: A has n linearly independent eigenvectors

An invertible matrix need not have n linearly independent eigenvectors; defective matrices are invertible but not diagonalizable.

Question 10: What is the relationship between theory and practice in Signal Processing?

Theory provides the foundation; practice applies it to real situations (Correct answer)
Theory is unnecessary
They are completely separate
Practice is unnecessary if you know theory

Correct answer: Theory provides the foundation; practice applies it to real situations

Theory provides the conceptual foundation and principles, while practice involves applying those concepts to real-world situations. Both are essential for competence.

Question 11: Which field studies the behavior of forces on structures?

Quantum physics
Fluid mechanics
Structural mechanics (Correct answer)
Thermodynamics

Correct answer: Structural mechanics

Structural mechanics is a specialized field within applied mechanics that focuses on analyzing the behavior of physical structures and their components under various loads and forces. It investigates how structures deform, experience stress, and strain to ensure their stability, strength, and rigidity. This discipline is crucial for the design and analysis of buildings, bridges, and other engineered systems.

Question 12: What is the law of conservation of energy?

Energy always decreases
Energy can be created from nothing
Energy is always increasing
Energy cannot be created or destroyed, only transformed (Correct answer)

Correct answer: Energy cannot be created or destroyed, only transformed

The law of conservation of energy states that the total energy in a closed system remains constant — it can change forms but cannot be created or destroyed.

Question 13: An NFA with n states can be converted to an equivalent DFA with at most how many states?

n
n²
2^n (Correct answer)
2n

Correct answer: 2^n

The subset construction algorithm for NFA-to-DFA conversion can produce up to 2^n states, one for each subset of the NFA's n states.

Question 14: What is thrashing in the context of virtual memory?

CPU spending more time on process execution
Too many processes waiting for I/O
Excessive disk I/O due to constant page swapping (Correct answer)
Memory fragmentation causing allocation failures

Correct answer: Excessive disk I/O due to constant page swapping

Thrashing occurs when a system spends more time swapping pages in and out of memory than executing actual process instructions.

Question 15: In the Banker's algorithm, a state is considered safe if:

No process is in the waiting state
All processes can be allocated their maximum resources immediately
There exists a sequence in which all processes can complete (Correct answer)
The total allocated resources equal total available resources

Correct answer: There exists a sequence in which all processes can complete

A safe state has at least one safe sequence where every process can eventually obtain its maximum needed resources and finish.

Question 16: What phenomenon explains why a pencil appears bent in water?

Reflection
Absorption
Refraction (Correct answer)
Diffraction

Correct answer: Refraction

Refraction is the phenomenon where light bends as it passes from one transparent medium to another, such as from air into water. This bending occurs because light changes speed when it enters a medium with a different optical density. When a pencil is partially submerged in water, the light rays from the submerged part bend differently than those from the part in air, causing the pencil to appear bent or displaced.

Question 17: How does documentation support quality in Signal Processing?

It is only for billing
It creates records, ensures consistency, and enables improvement (Correct answer)
Documentation is unnecessary overhead
It only serves administrative purposes

Correct answer: It creates records, ensures consistency, and enables improvement

Proper documentation creates accountability, ensures consistency, supports quality improvement, and provides legal protection.

Question 18: What is the primary purpose of professional certification in Control Systems?

To replace practical experience
To meet legal requirements only
To increase salary automatically
To validate competency and knowledge in the field (Correct answer)

Correct answer: To validate competency and knowledge in the field

Certification validates that a professional has met established standards of knowledge and competency in Control Systems.

Question 19: How does documentation support quality in Signal Processing?

It creates records, ensures consistency, and enables improvement (Correct answer)
It is only for billing
Documentation is unnecessary overhead
It only serves administrative purposes

Correct answer: It creates records, ensures consistency, and enables improvement

Proper documentation creates accountability, ensures consistency, supports quality improvement, and provides legal protection.

Question 20: Stokes' theorem relates a surface integral of the curl to:

A volume integral
A scalar field integral
Another surface integral of lesser dimension
A line integral over the boundary curve of the surface (Correct answer)

Correct answer: A line integral over the boundary curve of the surface

Stokes' theorem states ∬(∇×F)·dS = ∮F·dr, converting a surface integral of curl to a line integral around the boundary.

Question 21: Which study approach is most effective for Signal Processing material?

Passive re-reading of notes
Highlighting all text
Active recall with practice questions (Correct answer)
Studying for very long sessions without breaks

Correct answer: Active recall with practice questions

Active recall through practice questions is the most effective study method, as it strengthens memory retrieval pathways.

Question 22: What type of graph is best for showing trends over time?

Line graph (Correct answer)
Scatter plot
Bar graph
Pie chart

Correct answer: Line graph

Line graphs connect data points over time, clearly showing trends, patterns, and changes in data.

Question 23: Which method uses previous experience to solve new problems?

Deductive reasoning
Analogical reasoning (Correct answer)
Random guessing
Predictive analysis

Correct answer: Analogical reasoning

Analogical reasoning involves using knowledge and solutions from a past, similar problem (the source) to solve a new problem (the target). This method relies on identifying structural similarities between different situations and applying previously successful strategies or insights. It's a common cognitive process for making inferences and solving novel challenges based on prior experience.

Question 24: What is the general solution of a homogeneous linear differential equation?

Sum of complementary function and particular solution (Correct answer)
Only complementary function
Only particular solution
Zero always

Correct answer: Sum of complementary function and particular solution

The general solution of a linear differential equation, whether homogeneous or non-homogeneous, is composed of two parts: the complementary function and a particular solution. The complementary function solves the associated homogeneous equation, while the particular solution addresses the non-homogeneous part. For a strictly homogeneous equation, the particular solution is typically zero, making the complementary function the complete solution.

Question 25: What is root cause analysis?

Creating new problems
Identifying the primary reason for a problem (Correct answer)
Addressing symptoms only
Guessing the issue

Correct answer: Identifying the primary reason for a problem

Root cause analysis (RCA) is a systematic process for identifying the underlying, fundamental causes of a problem or undesirable event, rather than just addressing its symptoms. The goal of RCA is to implement solutions that prevent recurrence by eliminating the root cause. This leads to more effective and lasting problem resolution.

Question 26: In the method of least squares for curve fitting, the objective is to minimize:

The sum of residuals
The maximum residual
The sum of absolute residuals
The sum of squared residuals (Correct answer)

Correct answer: The sum of squared residuals

Least squares minimizes Σ(yᵢ - ŷᵢ)², the sum of squared differences between observed and fitted values.

Question 27: Which disk scheduling algorithm minimizes seek time by serving the closest request first?

FCFS
SSTF (Shortest Seek Time First) (Correct answer)
SCAN
C-SCAN

Correct answer: SSTF (Shortest Seek Time First)

SSTF selects the pending request closest to the current disk head position, minimizing individual seek times but potentially causing starvation.

Question 28: How does documentation support quality in Digital Logic?

Documentation is unnecessary overhead
It is only for billing
It only serves administrative purposes
It creates records, ensures consistency, and enables improvement (Correct answer)

Correct answer: It creates records, ensures consistency, and enables improvement

Proper documentation creates accountability, ensures consistency, supports quality improvement, and provides legal protection.

Question 29: Which scheduling algorithm can cause starvation of low-priority processes?

Shortest Job First (non-preemptive)
Round Robin
Priority Scheduling (Correct answer)
FCFS

Correct answer: Priority Scheduling

Priority Scheduling can starve low-priority processes indefinitely if high-priority processes keep arriving.

Question 30: What role does ethics play in Control Systems practice?

It only matters for legal compliance
It only applies to managers
Ethics is optional in professional settings
It guides professional conduct and protects stakeholders (Correct answer)

Correct answer: It guides professional conduct and protects stakeholders

Professional ethics provide frameworks for responsible decision-making, ensuring practitioners act in the best interest of those they serve.

Question 31: What is a heuristic approach in problem-solving?

Trial-and-error
Ignoring the issue
Using a simple, practical rule to solve a problem (Correct answer)
Mathematical proof

Correct answer: Using a simple, practical rule to solve a problem

A heuristic approach involves employing a practical, experience-based method or a 'rule of thumb' that is not guaranteed to be optimal or perfect, but is sufficient for reaching an immediate, short-term goal or approximation. Heuristics are mental shortcuts that simplify complex problems and allow for quicker decision-making, often when a complete or exhaustive solution is impractical.

Question 32: What is the range of the data set: 3, 7, 1, 9, 5?

8 (Correct answer)
7
5
9

Correct answer: 8

Range = maximum value - minimum value = 9 - 1 = 8.

Question 33: Which numerical method is used for solving ordinary differential equations?

Simpson’s Rule
Newton-Raphson method
Gaussian Elimination
Runge-Kutta method (Correct answer)

Correct answer: Runge-Kutta method

The Runge-Kutta method is a family of iterative numerical methods widely used to approximate solutions of ordinary differential equations (ODEs) with a given initial value. It is particularly valued for its accuracy and stability, making it a cornerstone in computational mathematics and engineering for modeling dynamic systems.

Question 34: What is the CIA triad in information security?

Certified Information Auditor
Confidentiality, Integrity, Availability (Correct answer)
Central Intelligence Agency
Cybersecurity Infrastructure Act

Correct answer: Confidentiality, Integrity, Availability

The CIA triad represents three core security principles: Confidentiality (keeping data private), Integrity (data accuracy), Availability (systems accessible when needed).

Question 35: What is the main purpose of brainstorming?

Focus only on one solution
Eliminate all bad ideas immediately
Generate multiple ideas quickly (Correct answer)
Avoid team collaboration

Correct answer: Generate multiple ideas quickly

Brainstorming is a group creativity technique designed to generate a large number of ideas in a short period, without initial judgment or criticism. Its main purpose is to encourage free-flowing thought and diverse perspectives, fostering an environment where quantity of ideas is prioritized over quality at the initial stage. This ultimately leads to a wider range of potential solutions.

Question 36: What is correlation?

An average value
Proof of cause and effect
A type of graph
A statistical relationship between two variables (Correct answer)

Correct answer: A statistical relationship between two variables

Correlation measures the strength and direction of a relationship between two variables, without implying that one causes the other.

Question 37: Read the passage: 'All employees who joined before 2010 are eligible for a pension. John joined in 2008.' Which conclusion is valid?

John is eligible for a pension (Correct answer)
John joined after 2010
John is not eligible for a pension
Nothing can be concluded

Correct answer: John is eligible for a pension

John joined in 2008, which is before 2010, so he meets the condition for pension eligibility.

Question 38: Which of the following sorting algorithms is both stable and guarantees O(n log n) worst-case time complexity?

HeapSort
Merge Sort (Correct answer)
Selection Sort
QuickSort

Correct answer: Merge Sort

Merge Sort preserves the relative order of equal elements (stable) and always runs in O(n log n); HeapSort is O(n log n) but not stable, and QuickSort degrades to O(n²) worst case.

Question 39: What is the next number in the sequence: 2, 4, 8, 16, __?

32 (Correct answer)
28
30
24

Correct answer: 32

The sequence 2, 4, 8, 16 follows a pattern where each number is obtained by multiplying the previous number by 2. This is a geometric progression with a common ratio of 2. Therefore, to find the next number, you multiply the last number (16) by 2, which gives 32.

Question 40: Which normal form ensures that a context-free grammar has no unit productions and no ε-productions (except possibly S → ε)?

Backus-Naur Form
Wirth Syntax Notation
Chomsky Normal Form (CNF) (Correct answer)
Greibach Normal Form (GNF)

Correct answer: Chomsky Normal Form (CNF)

Chomsky Normal Form requires all productions to be of the form A → BC or A → a, eliminating unit productions and ε-productions.

Question 41: A train travels 60 miles in 1.5 hours. What is its average speed?

30 mph
45 mph
40 mph (Correct answer)
50 mph

Correct answer: 40 mph

To find the average speed, you divide the total distance traveled by the total time taken. In this case, the train travels 60 miles in 1.5 hours. Therefore, the average speed is calculated as 60 miles / 1.5 hours = 40 miles per hour (mph).

Question 42: Which memory allocation strategy leads to external fragmentation?

Fixed partitioning only
Segmentation (Correct answer)
Virtual memory
Paging

Correct answer: Segmentation

Segmentation allocates variable-sized memory chunks, leading to external fragmentation as free memory becomes scattered in non-contiguous holes.

Question 43: The general solution of the second-order ODE y'' - 4y = 0 is:

y = C₁cos(2x) + C₂sin(2x)
y = (C₁+C₂x)e^(2x)
y = C₁e^(2x) + C₂e^(-2x) (Correct answer)
y = C₁e^(4x) + C₂

Correct answer: y = C₁e^(2x) + C₂e^(-2x)

The characteristic equation r² - 4 = 0 gives r = ±2, leading to y = C₁e^(2x) + C₂e^(-2x).

Question 44: What is the mode of: 2, 3, 3, 4, 5, 3, 6?

2
3 (Correct answer)
4
5

Correct answer: 3

The mode is the value that appears most frequently. The number 3 appears three times, more than any other value.

Question 45: In Unix, which system call creates a new process?

exec()
create()
fork() (Correct answer)
spawn()

Correct answer: fork()

The fork() system call creates a child process that is a copy of the parent process's address space.

Question 46: A sphere of radius r is inscribed in a cube. What is the ratio of the volume of the cube to the volume of the sphere?

π/3
3/π
6/π (Correct answer)
π/6

Correct answer: 6/π

Cube side = 2r; V_cube=(2r)³=8r³; V_sphere=4πr³/3; ratio=8r³/(4πr³/3)=6/π.

Question 47: If A is an invertible matrix, what is the determinant of A inverse?

det(A)^2
-det(A)
det(A)
1/det(A) (Correct answer)

Correct answer: 1/det(A)

For any invertible square matrix A, a fundamental property in linear algebra states that the determinant of its inverse, denoted as det(A⁻¹), is equal to the reciprocal of the determinant of the original matrix A. This relationship, det(A⁻¹) = 1/det(A), is crucial for calculations involving matrix inverses and understanding their properties.

Question 48: A sentence with a grammatical error: 'The committee have decided to postpone their meeting.' Choose the correction.

The committee has decided to postpone their meeting.
No error exists.
The committee have decided to postpone its meeting.
The committee has decided to postpone its meeting. (Correct answer)

Correct answer: The committee has decided to postpone its meeting.

'Committee' is a collective noun treated as singular in American English, requiring 'has' and the singular pronoun 'its'.

Question 49: If 5 pens cost $10, how much do 8 pens cost?

$15
$16 (Correct answer)
$14
$18

Correct answer: $16

First, determine the cost per pen: $10 divided by 5 pens equals $2 per pen. Then, to find the cost of 8 pens, multiply the cost per pen by 8. So, $2/pen * 8 pens = $16. Therefore, 8 pens would cost $16.

Question 50: Which page replacement algorithm suffers from Belady's anomaly?

Clock
FIFO (Correct answer)
LRU
Optimal

Correct answer: FIFO

FIFO can paradoxically increase page faults when more frames are added, a phenomenon known as Belady's anomaly.

Question 51: Which data structure is used in Breadth-First Search (BFS) to track the order in which vertices are visited?

Priority Queue
Deque
Stack
Queue (Correct answer)

Correct answer: Queue

BFS explores vertices level by level, requiring a FIFO queue so that nodes discovered earlier are processed before later-discovered nodes.

Question 52: According to Rice's theorem, which of the following is decidable?

Whether a Turing machine accepts a finite language
Whether a Turing machine halts on all inputs
Whether a Turing machine has exactly 5 states (Correct answer)
Whether a Turing machine accepts the empty string

Correct answer: Whether a Turing machine has exactly 5 states

Rice's theorem applies to non-trivial semantic properties of a TM's language; the number of states is a syntactic property of the TM itself, which is decidable.

Question 53: Which process state transition is NOT valid in a typical OS process state diagram?

Waiting → Running (Correct answer)
Ready → Running
Running → Waiting
Running → Ready

Correct answer: Waiting → Running

A process in the Waiting state must first move to the Ready state after its I/O completes before it can be scheduled to run again.

Question 54: What is a controlled variable in an experiment?

A factor kept constant to ensure a fair test (Correct answer)
An unexpected result
The variable being changed
The variable being measured

Correct answer: A factor kept constant to ensure a fair test

Controlled variables are kept the same throughout the experiment so that any changes in the dependent variable can be attributed to the independent variable.

Question 55: An epsilon-NFA (ε-NFA) differs from a standard NFA in that:

It allows transitions without consuming any input symbol (Correct answer)
It can have more than one start state
It requires a stack for computation
It cannot accept the empty string

Correct answer: It allows transitions without consuming any input symbol

An ε-NFA allows ε-transitions — state transitions that occur without reading any input character — which simplify grammar-to-automata conversions.

Question 56: What is the first step in problem-solving?

Identifying and understanding the problem (Correct answer)
Ignoring the issue
Testing random solutions
Finding a solution immediately

Correct answer: Identifying and understanding the problem

Before any solution can be sought, it is crucial to clearly identify and fully understand the problem at hand. This initial step involves defining the problem's scope, its symptoms, and its potential causes. A clear understanding ensures that efforts are directed towards solving the actual problem, rather than just its symptoms, leading to more effective and sustainable solutions.

Question 57: What is the difference between an element and a compound?

A compound is simpler than an element
An element contains multiple types of atoms
An element is a pure substance; a compound is two or more elements chemically combined (Correct answer)
They are the same thing

Correct answer: An element is a pure substance; a compound is two or more elements chemically combined

Elements consist of one type of atom (e.g., oxygen), while compounds are substances formed by chemical combination of two or more different elements (e.g., water = H₂O).

Question 58: What is the primary purpose of professional certification in Signal Processing?

To replace practical experience
To validate competency and knowledge in the field (Correct answer)
To meet legal requirements only
To increase salary automatically

Correct answer: To validate competency and knowledge in the field

Certification validates that a professional has met established standards of knowledge and competency in Signal Processing.

Question 59: What is the Laplace transform of 1?

s
s+1
s^2
1/s (Correct answer)

Correct answer: 1/s

The Laplace transform is an integral transform that converts a function of a real variable (often time, t) into a function of a complex variable (frequency, s). For the constant function f(t) = 1, its Laplace transform is 1/s. This is a fundamental result used extensively in solving linear differential equations and analyzing systems in engineering.

Question 60: Which quantity is conserved in all chemical reactions?

Volume
Mass (Correct answer)
Temperature
Density

Correct answer: Mass

The Law of Conservation of Mass states that mass is neither created nor destroyed in any chemical reaction or physical transformation within an isolated system. This means that the total mass of the reactants before a chemical reaction must always equal the total mass of the products after the reaction. It is a foundational principle in chemistry, ensuring that atoms are merely rearranged, not lost or gained.

Question 61: Which study approach is most effective for Digital Logic material?

Studying for very long sessions without breaks
Passive re-reading of notes
Highlighting all text
Active recall with practice questions (Correct answer)

Correct answer: Active recall with practice questions

Active recall through practice questions is the most effective study method, as it strengthens memory retrieval pathways.

Question 62: P is taller than Q. R is taller than P. S is shorter than R but taller than Q. Who is the shortest?

Q (Correct answer)
R
S
P

Correct answer: Q

Order: R>P>S>Q (since S>Q and P>Q and R>P>Q); Q is shortest.

Question 63: In the context of file systems, what does inode contain?

File content only
File name and directory path
User and group permissions only
File metadata and pointers to data blocks (Correct answer)

Correct answer: File metadata and pointers to data blocks

An inode stores file metadata (size, permissions, timestamps) and pointers to the actual data blocks on disk, but not the filename.

Question 64: If 8 workers can complete a job in 6 days, how many days would 4 workers take?

10 days
15 days
12 days (Correct answer)
9 days

Correct answer: 12 days

This is an inverse proportionality problem: the total amount of work (workers * days) remains constant. If 8 workers complete a job in 6 days, the total work is 8 * 6 = 48 'worker-days'. If only 4 workers are doing the job, they would take 48 worker-days / 4 workers = 12 days to complete the same job.

Question 65: What is the relationship between theory and practice in Signal Processing?

They are completely separate
Theory is unnecessary
Practice is unnecessary if you know theory
Theory provides the foundation; practice applies it to real situations (Correct answer)

Correct answer: Theory provides the foundation; practice applies it to real situations

Theory provides the conceptual foundation and principles, while practice involves applying those concepts to real-world situations. Both are essential for competence.

Graduate Aptitude Test in Engineering (GATE)

GATE is a national-level examination in India that primarily tests the comprehensive understanding of various undergraduate subjects in engineering and technology.

Questions

180 min

Time Limit

30%

To Pass

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Unanswered questions count as wrong — answer everything
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These practice questions were written with AI tools. They are not real exam questions. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy

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